Qualitative analyses of ecological models : an automated dynamical systems approach

• Main Author: Van Coller, Lynn
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/6299

Ecological models and qualitative analyses of these models can give insight into the most important mechanisms at work in an ecological system. However, the mathematics required for a detailed analysis of the behaviour of a model can be formidable. In this thesis I demonstrate how various computer packages can aid qualitative analyses by implementing techniques from dynamical systems theory. I analyse a number of continuous and discrete models to demonstrate the kinds of results and information that can be obtained. I begin with three fairly simple predator-prey models in order to introduce the terminology and techniques and to demonstrate the reliability of the computer software. I then look at a more practical system dynamics model of a sheep-pasture-hyrax-lynx system and compare the techniques with a traditional sensitivity analysis. A ratio-dependent model is the focus of the next chapter. The analysis highlights some of the biological implausibilities and mathematical difficulties associated with these models. Two discrete population genetics models are considered in the following chapters. The techniques are able to deal with the complex nonlinearities and lead to insights into the conditions under which stable homomorphisms and polymorphisms occur. The final example is a complicated discrete model of the spruce budworm-forest defoliating system. The mechanisms responsible for insect outbreaks and the relative effects of dispersal and predation are studied. In all the cases the techniques lead to a better understanding of the interactions between various processes in the system than was possible using traditional techniques. In two cases the results suggest improvements in the formulations of the models. The techniques also identify parameters or processes which are crucial for determining model behaviour. All these results are obtained fairly easily with the use of the computer packages and do not require an extensive mathematical knowledge of dynamical systems theory or intensive mathematical manipulations.